PEST++IES how many iterations & realizations, finding the point of diminishing returns

PEST++IES (White 2018; White et al. 2020) is widely used in the groundwater modeling community for its ability to perform computationally efficient history matching and uncertainty analysis in a highly parameterized context. One primary advantage of using an iterative ensemble smoother is that the number of model runs required per iteration depends on the number of realizations in an ensemble, not the number of parameters in each realization. However, this raises the question: what is the optimal number of realizations and iterations to use for any one model before the point of diminishing returns? Using a modified version of the Freyberg model (Freyberg 1988; Hunt et al. 2020), different parameter and observation scenarios were evaluated for four iterations and ensembles of 10, 25, 50, 100, 250, 500, 1000, and 2000 realizations. To match observations, PEST++IES altered hydraulic conductivity (k), both globally across the model and locally at three different pilot point densities, as well as global recharge (via a single multiplier), global river conductance, and individual well flow rates. Risk-based well capture zone results (Fienen et al. 2022a) and estimated hydraulic conductivity fields from each scenario were quantitatively and qualitatively compared against the “truth” model and its outputs. Across the cases examined, ensemble sizes of 100 to 250 realizations and two PEST++IES iterations were generally sufficient to achieve good results.